Thank you Q and Gargoyle. There are quite a few fragments of songs in Opie. There is a reference to James Orchard Halliwell's collection's of nursery rhymes, and I really should try to find his books. The Opie's say that: "Whether they (crow-scaring songs) were considered to be nursery rhymes before JOH included them in his collection is doubtful..."
I have seen the rhyme that you mention.
I have a reference in Opie to the Crow being called "John Crow" but so far nothing to confirm my father's statement that "Jim Crow" was a name for the Crow.
Another digression - there is a magpie on my head but she's no help.